Abstract

Light is critical for art. It allows us to see color, and can itself be a tool for creating unique pieces of art and design. Here we demonstrate that a laser can be a multifunctional and effective tool for the creation of masterpieces, analogous to the process of an artist creating a canvas with classical paints and brushes. We investigate the interaction between focused laser irradiation and metallic surfaces and analyze the optical effects in thin oxide films for three main artistic operations: color making, multiple color changes, and erasing managed by a nanosecond laser. These processes are possible upon heating the material above the evaporation point and are proved to be dependent on the cooling rate, according to both experimental and theoretical results. Such an interference-based laser paintbrush could find applications in modern art and design.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

From the early days people have encoded messages by drawing primitive pictures and patterns on rocks, and they have created small drawings and toys to describe the world around them. Then, step by step, ancient art and painting were born. Gradually, the progress of tools and human thought led to a symbiosis of art and technology; one of the brightest examples is Leonardo da Vinci’s heritage. Nowadays, with the rapid development of technologies and industry, the evolution of contemporary art is taking place, and novel artistic techniques are being introduced by modern artists from all over the world.

The most common artistic materials are oil paints, watercolors, inks, pastel, charcoal, etc. Let us consider different ways of creating a colorful image without using any of these usual colorants. Obviously, different optical effects such as interference; diffraction; near-field, far-field, and nonlinear effects; collective resonances, and so on can act as effective tools for obtaining a color palette [115]. For instance, plasmonic nanostructures absorb and re-emit the light at the specific wavelengths due to localized surface plasmon resonance [5,6,16,17]. Also, various semiconductor or all-dielectric nanostructures possessing minimal losses in the visible spectrum produce color due to arising of magnetic and electric dipole resonances [9,1820]. Color change is possible by manipulation of size, shape, and distribution of nanostructures, and a number of researches have already described various approaches, for example, chemical synthesis [1,21,22], lithography methods [2,11,12,19], focused ion beam milling [13], and laser-based fabrication [4,14,17,23,24]. Other groups of works [2528] have described color creation on micro- and nanogratings by diffraction effects. But such diffraction patterns usually exhibit a certain color only when viewed from a predetermined angle. Another broad group of promising dye-free coloration techniques uses different coatings and interference films [1,2831]. To apply a colorful picture on different materials, the method of colloidal ink jet imprinting has been recently developed [29,31]. The method is based on application of colloidal film with a given thickness. Despite the obvious pros of the discussed color printing methods (like bright colors and ability to control spectra with high accuracy), most of the mentioned techniques are still time-consuming, costly, and may appear unstable in the long run. Thus, they are applicable only for small-scale short-lived images. It is important to note that all the considered methods are nonreversible, which means it is still challenging to rewrite or erase the color if an artist makes a mistake or decides to change the original idea.

Laser oxidation of metals is known to be a promising way of controlled color creation, which offers fast, large-scale, and eco-friendly writing of colorful pictures. Local manipulation with colors is handled by precise tuning of an oxide thickness and chemical composition [30,3237] as well as treatment environment [38,39]. Another work introduced the computational algorithms to provide good color image reproduction; moreover, the authors managed over seven different laser processing parameters to expand and systematize the color gamut on stainless steel [40]. On titanium surfaces different color palettes were also developed by several research groups [32,39]. We have recently demonstrated that such colors on titanium surface are extremely resistant to environmental and chemical impacts [41], and therefore a laser-induced picture is everlasting and does not require any special storage environment. All of these facts show the great potential of laser oxide-based coloration for industrial applications; nevertheless, the possibility of laser painting for art is still pending. To paint an authentic picture, one need not only be able to apply a color according to the template but also to change and manage colors up to their complete erasure. At the same time, mechanisms and principles that make change and erasure of the interference-based structural colors in air possible have not yet been investigated.

Our article presents for the first time to our knowledge the laser treatment as a paintbrush for creation the colorful images, or “paintings” on the titanium surface. We concentrate on different ways of creating an image following the conventional steps of an artist: making color strokes, changing the color, and erasing some fragments. Here we expand the opportunities of laser coloration by representing all these actions by fast laser writing on a titanium surface and describe the mechanisms behind this technique, including local laser heating, laser oxidation, and erasing of the oxide film. In order to investigate these processes, we perform detailed analysis of physical and chemical processes under laser irradiation based on experimental and numerical results. As opposed to previous works, we consider the process of laser heating above the metal evaporation temperature. Vaporization is then followed by metal oxidation at the cooling stage, and the resulting color forms during the temperature dropping. This oxidation regime makes it possible to either rewrite or erase colors by varying the cooling rate. We also consider the optical effects on oxide films depending on their thickness using the theory of wave propagation through a stratified semitransparent film on an opaque substrate. The possibility of rewriting or erasing colors in an airy atmosphere would take laser coloring to a new level, allowing not only reproduction of already known images from a template but also modification of an image during the drawing process according to the wishes of an artist. We believe that laser paintbrush technique will pave the way for creating a new kind of modern art and design.

2. MATERIALS AND METHODS

A. Laser Fabrication of Color Miniature Painting

A nanosecond ytterbium fiber laser system equipped with a two-axis galvanometric scanner was used to create color strokes as well as to erase and rewrite color. The laser miniature painting was drawn on a 1 mm thick titanium alloy (Ti6Al4V) polished plate, cleaned with ethanol before using. A F-theta lens ensured the uniform focalization of laser beam within the area of $110 \times 110\; {\rm mm}$. A focused Gaussian beam with a spot diameter of ${d_0} = 50\,\,\unicode{x00B5}{\rm m}$ scans the sample line by line, providing the defined overlap between two lines (for details see also [30]). During all the experiments pulse duration of $\tau = 100\; {\rm ns}$, laser intensity $I = 1.02 \cdot {10^7} \;{\rm W}/{\rm cm^2}$, repetition rate $f = 900\;{\rm kHz}$, and number of pulses along the $y$ axis ${N_y} = 1$ remained the same, whereas the scanning speed ${V_{\textit{sc}}}$ varied within the range of $100 {-} 1500\;{\rm mm/s}$ to obtain different effects.

B. Numerical Simulation

Numerical simulations of the reflectance spectra were conducted based on a theory of wave propagation through a stratified semitransparent medium described in [42]. The modeling was carried out within the range of 300–1100 nm. Spectral values of the complex refractive indices $n_{{j}}^\prime = {n_j} + i{k_j}$ were taken in accordance with [43] for titanium alloy Ti6Al4V and [4447] for titanium oxides ${\rm TiO_2}$ and ${\rm Ti_3}{\rm O_5}$. The temperature distribution was calculated by numerical finite-difference solving of the nonstationary nonlinear three-dimensional heat conduction equation with corresponding boundary and initial conditions. The heat capacity and heat conductivity of titanium temperature dependencies were taken from [48]. The reflection coefficient of Ti at wavelength 1.06 µm was considered equal to 0.56 [49]. Latent heat of melting ${L_m} = 1.3 \cdot {10^3} {\rm J}/{\rm cm^3}$ and latent heat of evaporation ${L_{{e\nu}}} = 4 \cdot {10^4} {\rm J}/{\rm cm^3}$ were taken from [48]; ${v_{{e\nu}}}$ is the evaporation rate that was considered in the Hertz–Knudsen approximation (see for example [50]).

C. Measurements

To examine microscopic appearance of color strokes, a Zeiss Axio Imager A1 m optical microscope was utilized in a reflection configuration. To measure reflectance spectra of the laser irradiated areas, we used the SF-56 spectrometer with an unpolarized light source. The atomic force microscope Nanoeducator was used to investigate surface topology after laser irradiation. To investigate the composition and crystalline phase of the color strokes, transmission electron microscopy (TEM) and the transmission scanning electron microscopy (SEM) were used. The Tecnai G2 F20 microscope with field emission equipped with an EDAX c microanalysis system and silicon drift detector was utilized. Ion thinning by a focused ion beam (FIB) on an Zeiss Auriga SEM was utilized for the preparation of thin foils (lamellas) for TEM. The detailed description of the lamella preparation process is presented in Supplement 1 (section “Sample Preparation for TEM”). As a result, square samples of approximately $3\;\unicode{x00B5}{\rm m^2}$ with a thickness of approximately 100 nm were obtained.

3. RESULTS

A. Concept and Design

Three basic techniques were developed for laser painting: (i) creating colors or individual color strokes, (ii) color mixture or changing one color to another, and (iii) color erasing. We call these three operations altogether the “laser paintbrush.” The schematic of the laser paintbrush technique is shown in Fig. 1. Colors were formed, changed, and erased on the titanium surface by single step laser scanning (see Section 2, Materials and Methods, for details). A laser beam scanned the surface line by line with different scanning speeds. In general, this process is rather fast (average productivity is $1.1 {-} 12.5\;{\rm cm^2}$ per min, depending on the color) and does not require any additional pretreatment, chemicals, or special environment.

 figure: Fig. 1.

Fig. 1. Schematics of laser paintbrush and microimages of color strokes.

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 figure: Fig. 2.

Fig. 2. Principle of color laser paintbrush. (a) Applying of color strokes: schematics of the process and photo of the color palette for titanium: laser intensity $I = 1.02 \cdot {10^7} \; {\rm W}/{\rm cm^2}$, and scanning speed decreases from 500 to $100\;{\rm mm/s}$ with the step of $50\;{\rm mm/s}$ for colors ${\rm Ti_1}$ to ${\rm Ti_9}$, respectively. (b) Reflectance spectra of the obtained color palette. (c) Color palette on color locus. (d) Schematics of laser rewriting and photo of color rewriting: eight identical areas of ${{\rm Ti}_8}$ color were initially obtained. After that, the second laser pass ($I = 1.02 \cdot {10^7} \; {\rm W}/{\rm cm^2}$) with the scanning speed in the range of 100–1500 mm/s was performed; the intersection area surrounded by black dashed line represents the corrected color. (e) Schematics of laser color erasing, photo, and microimages of color erasing of different colors ${\rm Ti_2} - {\rm Ti_9}$ performed at scanning speed ${V_{\textit{sc}}} = 1500\; {\rm mm/s}$ ($I = 1.02 \cdot {10^7}\; {\rm W}/{\rm cm^2}$).

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B. Applying of Individual Color Strokes

The first step of laser painting is the formation of color strokes on titanium surface. We define color strokes as a combination of surface relief and optical effects that allow us to visually observe areas of different colors (Fig. 1). Figures 2(a)–2(c) demonstrate the obtained color palette on titanium and reflection spectra after laser treatment. Depending on the laser processing parameters, the thickness of the obtained oxide film differed, leading to color change [Fig. 2(a)]. With the constant laser intensity of $1.02 \cdot {10^7} {\rm W}/{\rm cm^2}$, repetition rate $f = 900\;{\rm kHz}$, pulse duration $\tau = 100\; {\rm ns}$, and variable scanning speed in the range of 100–500 mm/s, nine basic colors were drawn. Figure 2(a) also demonstrates the photo of the developed color palette. The reflectance spectra of the developed color strokes are shown in Fig. 2(b). Reflection spectra minima shifted to the infrared region with the decrease of scanning speed, and the width of the maxima increased. After decreasing the scanning speed below 150 mm/s, the spectrum became smoother without any distinguishable peaks. The developed color palette was represented on the color locus [Fig. 2(c)]. As we can see from Fig. 2(c), color coordinates of ${\rm Ti_1} - {\rm Ti_9}$ color strokes move in a clockwise direction following the elliptic trajectory. Corresponding CIE ${\rm L*a*b*}$ (2013) color coordinates (for a D65 light source) of the developed color palette are listed in Table S1 in Supplement 1. To investigate the observed spectral tendency, we performed the simulation of the reflection coefficient. Characteristics of the obtained oxide layer varied depending on laser processing parameters. We identified two types of structures: a ${\rm TiO_2}$ rutile film with the average thickness of $20 \pm 3\; {\rm nm}$ and a double-layer structure consisting of an inner ${\rm TiO_2}$ anatase film $12 \pm 2\; {\rm nm}$) and an outer ${\rm Ti_3}{\rm O_5}$ film of $23 \pm 3\; {\rm nm}$ (the detailed experimental analysis of the laser-induced oxide layers is performed in Section 3.D, “Oxide Morphology”). Therefore, we considered the oxide layer on a titanium surface as a multilayer thin film system for which a characteristic matrix could be compiled [42]. For a two-layer system, the characteristic matrix is represented as follows:

$$M = \left[{\begin{array}{*{20}{c}}{\cos({\beta _1}) \cdot \cos({\beta _2}) - \frac{n_2^\prime}{n_1^\prime} \sin({\beta _1}) \cdot \sin({\beta _2})}&\quad\quad {- i \left(\frac{{\sin({\beta _2}) \cdot \cos({\beta _1})}}{n_2^\prime} + \frac{{\cos({\beta _2}) \cdot \sin({\beta _1})}}{n_1^\prime}\right)}\\[3pt]{- i({n_2^\prime} \sin({\beta _2}) + \cos({\beta _1}){n_1^\prime} \cos({\beta _2}) \cdot \sin({\beta _1}))}& \quad\quad{\cos({\beta _1}) \cos({\beta _2}) - \frac{n_2^\prime}{n_1^\prime} \sin({\beta _1}) \cdot \sin ({\beta _2})}\end{array}} \right],$$
where ${\beta _1} = 2\pi /\lambda n_j^\prime{h_j}$, $j = 1$ for ${{\rm Ti}_3}{{\rm O}_5}$, $j = 2$ for anatase ${{\rm TiO}_2}$, $n_{\!j}^\prime$ is the complex refractive index, and ${h_j}$ is the thickness of each layer. Considering the substrate with the complex refractive index ${n_{3}^\prime}$ and the ambient medium with ${n_{0}^\prime} = 1$, the reflectance of such system is derived as follows [42]:
$$R(\lambda ,{h_j}) = \left|\frac{{{M_{1,1}} + {n_3}{M_{1,2}} - {M_{2,1}} - {n_3}{M_{2,2}}}}{{{M_{1,1}} + {n_3}{M_{1,2}} + {M_{2,1}} + {n_3}{M_{2,2}}}}\right|^2,$$
where ${M_{m,l}}$ is the element of matrix $M$ in the $m$th row and $l$th column.

Reflectance spectra for a single layer of rutile ${{\rm TiO}_2}$ on the bulk Ti substrate can be derived similarly. The decrease of scanning speed leads to development of surface roughness, and thus the strokes recorded in low-speed regimes (${T_5} - {\rm Ti_9}$) possessed enhanced diffuse scattering (see Supplement 1, Fig. S1) that was not taken into account in the calculations. To compensate for this, the estimations of reflectance spectra were corrected according to the ratio of diffuse reflection to specular reflection (see Supplement 1). As a result, calculated spectra were decreased by 1.31 for the ${\rm Ti_4}$ color stroke and by 2.81 for the ${\rm Ti_8}$ color stroke.

The comparison between measured and modeled reflection spectra is shown in Fig. S2. The calculated spectra show a good agreement with the experimental curves, and the calculated color coordinates for both experimental and modelled curves occupy similar areas on the color locus. Thus, the observed redshift was proved to be related to the increase of the oxide film thickness. Moreover, the performed numerical analysis allowed us to make assumptions about the thicknesses of oxide layers in all the recording regimes. These values were estimated to vary from $15 \pm 2\;{\rm nm} $ to $30 \pm 3\;{\rm nm} $ of the ${\rm TiO_2}$ rutile layer for the ${\rm Ti_1} - {\rm Ti_6}$ regimes and from $11 \pm 2\;{\rm nm} $ to $20 \pm 3\;{\rm nm} $ of the ${\rm TiO_2}$ anatase layer underneath the ${\rm Ti_3}{\rm O_5}$ layer (from $21 \pm 3\;{\rm nm} $ to $40 \pm 5\;{\rm nm} $ thick) for the ${\rm Ti_7} - {\rm Ti_9}$ regimes (for details see Fig. S2 in Supplement 1).

C. Color Erasing

Using these basic strokes under precise control of laser processing parameters suffices to draw a colorful picture. But what to do if the obtained color differs from the desired one? We noticed that the second laser pass with the increased scanning speed up to 700 mm/s led to the reduction of color brightness. Furthermore, the retreatment with the intensity $I = 1.02 \cdot {10^7} \;{\rm W}/{\rm cm^2}$ and scanning speed ${V_{\textit{sc}}} = 1000 - 1500\; {\rm mm/s}$ caused the complete disappearance of visible color on the surface [Fig. 2(e)]. This effect was observed for all primary colors. The reflection spectra of the erased areas are demonstrated in Fig. S4(a). After laser erasing, the surface color was indistinguishable from a nontreated surface. The moderate differences of the spectra related to surface relief formed after laser treatment.

D. Changing of Color Strokes and Multiple Rewriting

Retreatment allowed us not only to completely erase color but also change it under certain conditions. Figure 2(d) shows the result of rewriting of color ${\rm Ti_8}$ (top line) by retreatment with the scanning speed ranged from 100 to 1500 mm/s (bottom line). Taking one more step in laser processing led to gradual change of color (rewriting zone). Figure S4(b) demonstrates the reflectance spectra of the rewritten colors that appeared to be similar to that the considered above. Thus, it was possible to obtain the same color palette as on the single-processed areas.

By combining all the results presented above, we developed the color palette on a titanium surface depending on laser scanning speed for the constant laser intensity $I = 1.02 \cdot {10^7}\; {\rm W}/{\rm cm^2}$ [Fig. 3(a)]. In Fig. 3(a), the areas surrounded by dashed lines show the resulting colors. The zone for coloring represents the scanning speed range for bare titanium. The rewriting zone is different for various initial colors. For instance, to make purple color (${\rm Ti_7}$) from light blue (${\rm Ti_8}$), the scanning speed of about 250 mm/s should be used. The erasing zone lies in the region of scanning speeds higher than 1200 mm/s. The decay of lines is related to the change in absorption for the pretreated area due to the primary oxidation.

 figure: Fig. 3.

Fig. 3. Color maps for laser painting, color change, and erasing for $I = 1.02 \cdot {10^7} \; {\rm W}/{\rm cm^2}$. (a) Color palette of the laser paintbrush. The map represents color dependencies on different scanning speed: the single-step coloration regime on a bare titanium (coloring zone), the change of eight initial colors for other ones (color change zone), complete erasing of colors (erasing zone). (b) Multiple rewriting of the color circle: colors are changed in a consequence, the result after initial writing (first pass), and rewriting (second and third passes).

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Each color was shown to be changed into another one according to the proposed map. Figure 3(b) shows the result of the rewriting of 10 color sectors after two and three additional laser passes: each sector changes color to the neighboring one in a clockwise direction as a result of laser retreatment. Multiple rewriting was possible for all the color strokes from Fig. 2(a) [see “Supplement 1, Fig. S5(b)]. Thus, the color change was carried out several times in a row.

Therefore, the multiple rewriting of colors is also possible. Figure 4(a) shows the schematics of the experiment. First, the big square ($25 \times 25\; {\rm mm}$) was drawn with the scanning speed of 350 mm/s [equal to the ${\rm Ti_4}$ regime, which is shown above in Fig. 2(a)]. Then we partially overwrote the gold square with the scanning speed of 170 mm/s, resulting in the smaller blue square (L2, L4, L6, L8). To go back to a gold square again, the counteracting laser treatment with the scanning speed of 450 mm/s (L3, L5, L7, L9) was applied. Nine cyclical writing and rewriting steps were performed [Fig. 4(b)] in total. Figure 4(c) presents measured reflection spectra of the processed areas [Fig. 4(c)]. From these curves, the color differences $\Delta E$ were then calculated for all gold and all blue samples, and $\Delta E$ was proved to be less than 8, which confirms that the difference in color cannot be seen with the naked eye.

 figure: Fig. 4.

Fig. 4. Multiple color rewriting. (a) Schematics of laser multiple rewriting of gold color to blue and back. (b) Photo of rewritten squares: Layer 1 (${\rm L}1$) reproduces sample ${\rm Ti_4}$ (${I} = 1.02 \cdot {10^7}\; {\rm W}/{\rm cm^2}$, ${V_{\textit{sc}}} = 350\; {\rm mm/s}$). All the blue layers (${\rm L2,L4,L6,L8}$) were produced by reprocessing of gold areas with a scanning speed of ${V_{\textit{sc}}} = 170\; {\rm mm/s}$. The ${\rm L3,L5,L7,L9}$ gold layers were recorded with a scanning speed of ${V_{{sc}}} = 450\;{\rm mm/s}$. (c)–(e) Reflectance spectra of colors: (c) experimental spectra, ${\rm L1 - L9}$: color difference between the rewritten colors $\Delta E$ does not exceed 8; (d) colors representing experimental and calculated CIE ${\rm L*a*b*}$ (2013) color coordinates for initial surface (${\rm Ti_0}$) L1 and L8; (e) modelled spectra: the yellow line is for the ${\rm L}1$ regime (estimated for $20 \pm 3\;{\rm nm}$ thick rutile film on a bulk Ti), the and blue line is for the ${\rm L}8$ regime (estimated for $23 \pm 3\;{\rm nm}$ thick ${\rm Ti_3}{\rm O_5}$ and $12 \pm 2\;{\rm nm}$ thick anatase films layered on top of a bulk Ti). (f)–(h) Morphological and structural characterization of oxide layers after laser exposure. TEM, STEM, and electron beam diffraction images of oxide films of samples: (f) ${\rm L}1$, (g) L9, and (h)${\rm Ti_8}$.

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With the larger numbers of rewriting steps (up to 30), visually observed color also did not change [see Supplement 1, Fig. S5(a)]. We assume that the maximum number of color rewriting cycles is limited mostly by the titanium plate thickness, taking into account the average thickness of the removed material layer for each cycle. The surface profile after a single laser pass in Fig. 5(a) shows that this thickness is usually less than $1.5\,\,\unicode{x00B5}{\rm m}$ for the ${\rm Ti_7}$ regime; thus, more than 500 rewriting cycles is possible.

 figure: Fig. 5.

Fig. 5. Temperature distribution and laser oxidation process. (a) Microimage and profile of Ti surface after laser irradiation; (b) calculated temperature distribution over the surface; (c) temperature dynamics for central region of the recorded track considering the presence of oxide layers for different scanning speeds (${I} = 1.02 \cdot {10^7} \;{\rm W}/{\rm cm^2}$).

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E. Oxide Morphology and Composition

The morphology and composition of the interference films grown on the top of titanium surface were then investigated by means of transmission electron microscopy. Morphology and diffraction analysis of lamellae etched from two gold squares, which are L1 [Fig. 4(f)] and L9 squares [Fig. 4(g)], and a blue one, the ${\rm Ti_8}$ square [Fig. 4(h)], were performed. Figure S8 in Supplement 1 show the lamella preparation process.

According to TEM (in bright-field and dark-field contrast), the thicknesses of the oxide layers for the gold-colored samples ${\rm Ti_4}$ (L1 obtained after a single pass by laser radiation and L9 obtained after nine passes) were the same and equal to $20 \pm 3\; {\rm nm}$ [Figs. 4(f) and 4(g), respectively]. The thickness of the ${\rm Ti_8}$ blue oxide layer obtained after a single pass proved to be $35 \pm 5\; {\rm nm}$ [Fig. 4(h)]. The slight variation of the thickness reflected the inhomogeneous temperature distribution due to the Gaussian beam profile and variable overlap between laser spots. Microphotographs of laser-treated areas (see Fig. S3 in Supplement 1) indeed show color inhomogeneities. High-resolution electron microscopy showed that the oxide layers of gold colors appeared after one and nine passes (L1 and L9) had lattice parameters of titanium dioxide ${\rm TiO_2}$ (rutile). The ${\rm Ti_8}$ sample was shown to consist of two layers: the inner layer of ${\rm TiO_2}$ (anatase) and the outer layer of ${\rm Ti_3}{\rm O_5}$. These sublayers’ thicknesses were $12 \pm 2\; {\rm nm}$ and $23 \pm 3\; {\rm nm}$, respectively. The experimental and reference data on the lattice parameters of ${\rm TiO_2}$ (rutile), ${\rm TiO_2}$ (anatase), and ${\rm Ti_3}{\rm O_5}$ are presented in Table S3 in Supplement 1.

Known thickness and composition of oxide films after multiple rewriting allowed us to model the reflection spectra for L1 and L8 [Fig. 4(e)]. For the calculations, we considered that the composition of the L8 sample was equal to ${\rm Ti_8}$, and the thicknesses were taken within the experimentally measured interval. Measured spectra of the initial titanium surface as well as of colors L1 and L8 were compared to the calculated ones. To visualize the corresponding colors, CIE ${\rm L*a*b*}$ (2013) color coordinates were calculated (listed in Supplement 1, Table S2), and the colors are demonstrated in Fig. 4(d).

F. Insights into Laser Painting, Erasing, and Rewriting

For the simulation of Ti plate heating, we solved the nonstationary nonlinear three-dimensional heat conduction equation with corresponding boundary and initial conditions:

$$\begin{split}&{(c + {L_m}\delta (T - {T_m}))\frac{{\partial T}}{{\partial t}} - \nabla (k\nabla T) = 0}\\& - \left.k\frac{{\partial T}}{{\partial z}}\right|_{z = 0} = A\sum\limits_{i = 0}^{N - 1} {q_i} - {\nu _{{e\nu}}}{L_{{e\nu}}}\quad k\left.\frac{{\partial T}}{{\partial x}}\right|_{x = 0} = 0\quad k\left.\frac{{\partial T}}{{\partial y}}\right|_{y = 0} = 0\\ &\left.k\frac{{\partial T}}{{\partial z}}\right|_{z = {z_{{\max}}}} = 0\quad k\left.\frac{{\partial T}}{{\partial x}}\right|_{x = {x_{{\max}}}} = 0\quad k\left.\frac{{\partial T}}{{\partial y}}\right|_{y = {y_{{\max}}}} = 0\\ &\left.T\right|_{t = 0} = {T_0},\end{split}$$
where $T = T(x,y,z,t)$ is the temperature distribution, ${q_i} = {q_i}(x,y,t)$ is the intensity distribution for the $i$th pulse, and $c = c(T)$ and $k = k(T)$ are the volumetric heat capacity and heat conductivity of titanium, respectively. $A = 1 - R$ is the absorptance ($R$ is the reflection coefficient of Ti at wavelength 1.06 µm), ${{L}_m}$ is the latent heat of melting, ${{L}_{{e\nu}}}$ is the latent heat of evaporation, ${\nu _{{e\nu}}} = {\nu _{{e\nu}}}(T(x,y,0,t))$ is the evaporation rate taken in the Hertz–Knudsen approximation, and ${T_0} = 293\; {\rm K}$ is the initial temperature.

Note that in the temperature estimations for a single track, the bottom edge of the plate should not be heated significantly since the condition ${z_{\rm{max}}} \gg \sqrt {at}$ (${z_{\rm{max}}} = 1\;{\rm mm}$ is the thickness of the titanium plate, $a = k/c \sim {10^{- 5}}\; {\rm m^2}/{\rm s}$ is the thermal diffusivity, $t \sim d/{V_{\textit{sc}}}$ is the duration of thermal action, where $d$ is the laser beam diameter, and ${V_{\textit{sc}}}$ is scanning speed) is satisfied. Thus, one can apply the heat insulator conditions on the bottom edge of a plate neglecting the heat transfer to the substrate.

Functions ${q_i}$ were given by equations that correspond to multipulse laser heating with Gaussian beam scanned along the $x$ axis. (See details in Supplement 1, section “Temperature Dynamics of Laser Paintbrush Technique”).

First, the temperature distribution for laser painting mode was estimated. The titanium temperature was calculated for a single-track mode (${I} = 1.02 \cdot {10^7} \; {\rm W}/{\rm cm^2}$, $f = 900\; {\rm kHz}$, ${V_{\textit{sc}}} = 100,200,300\; {\rm mm}/{\rm s}$) considering the initial absorption capacity of untreated material. To identify the processes that took place under the laser irradiation, the surface temperature distribution was matched with the experimentally observed morphology of the titanium surface after laser irradiation. Figure 5(a) represents the optical microimage of a single track written at ${V_{\textit{sc}}} = 200\; {\rm mm}/{\rm s}$ and the height topology of this track measured by atomic force microscopy. For the same processing mode, the surface temperature distribution was calculated at $t = 0.85\; {\rm ms}$ when the maximum temperature was achieved [Fig. 5(b)]. Figure 5(b) shows that the temperature in the center of the track is much higher than the melting point (${T_m} = 1923\; {\rm K}$), namely, about 3900 K. Indeed, from analyzing the microphotography and the profile we concluded that intense evaporation in the center of the laser track occurred (when temperatures were higher than 3000 K).

The intensive oxidation process started at the heating stage when the temperature reached half of the melting point for titanium. However, when the temperature increased over the evaporation point, this oxide was obviously evaporated. The resulting oxide layer was grown at the cooling stage, and its thickness depended on the cooling time.

Based on the described approach and experimental data, we extended the model to experimentally analyze the obtained effects of color rewriting and color erasing. For this analysis, temperature distribution was calculated taking into account the presence of oxide film, which was grown after the first laser pass (considering the reflection coefficient equal to that for ${\rm Ti_7}$ and ${\rm Ti_8}$ modes at 1.06 µm). Thus, we estimated that (i) the initial absorption capacity increased about 2 times (for $\lambda = 1.06\,\,\unicode{x00B5}{\rm m}$) and (ii) after evaporation of the oxide film with the thickness of 30–40 nm, the initial absorption capacity of the surface relapsed to the initial value (for a bare titanium surface).

The results of the calculations for three different scanning speeds are presented in Fig. 5(c). Scanning speeds were chosen according the experimental results for the laser erasing mode (${V_{\textit{sc}}} = 1000\; {\rm mm/s}$), laser rewriting mode (${V_{\textit{sc}}} = 200\; {\rm mm/s}$), and threshold mode when the erasing effect just started (${V_{\textit{sc}}} = 600\; {\rm mm/s}$). As we can see from Fig. 5(c), due to enhanced surface absorption, the heating starts rather fast until the evaporation of the initial film, which is followed by a surge of temperature. Then the absorption capacity drops down to the values of the bare titanium surface and further heating dynamics become rather moderate. However, cooling times for the three processing modes were significantly different. Since the temperature reached a value above the evaporation point, the resulting oxide film growth occurred at the cooling stage. It is known that intensive oxidation of metals starts when the temperature is above half of the melting point [51]. Thus, in our case, the oxidation took place only when the temperature was between the evaporation and oxidation points. We set this time as an oxidation time ${t^*}$. At the scanning speed related to color rewriting mode, the oxidation time reached the value of $t_{200}^* = 680\; \unicode{x00B5}{\rm s}$. For laser erasing mode the temperature dropped sharply, and thus the oxidation time was $t_{1000}^* = 160\; \unicode{x00B5}{\rm s}$. It was estimated experimentally that the interplay between these two modes was found to be 600 mm/s for the given regimes. Therefore, the minimal oxidation time that was enough for color appearance was $t_{600}^* = 240\; \unicode{x00B5}{\rm s}$.

In general, it is possible to explain the coloration condition as follows:

$$\frac{{2 \cdot {{10}^{- 5}}I + 393}}{{{V_{\textit{sc}}}}} \gt 1,$$
where I is in ${\rm W}/{\rm cm^2}$, ${V_{\textit{sc}}}$ is in mm/s, and it is assumed that the other conditions correspond to experimental ones described earlier.

The equation is relevant for the color rewriting mode (after ${\rm Ti_7} - {\rm Ti_8}$ regimes) taking into account that oxidation time for rewriting is 1.2 times higher than for bare titanium. The coloration of titanium occurs when this inequality is valid. The formula above is empiric and relevant at least for $100 \lt {V_{\textit{sc}}} \lt 1500\; {\rm mm/s}$ and $9 \cdot {10^6} \lt I \lt 1.2 \cdot {10^7} \; {\rm W}/{\rm cm^2}$. See Supplement 1 section: “Temperature Dynamics of Laser Paintbrush Technique” for the detailed description of this equation.

G. Laser Paintings

The use of a laser as an artistic tool allows us to bridge the gap between art and science. Our main idea is to represent artist’s movements (painting color strokes, mixing colors, and erasing some strokes) by laser operations. Laser painting with individual color strokes allows us to make colorful paintings on a titanium “canvas” as shown in Fig. 6(a). Figure 6(b) illustrates the process of a laser painting of an abstract miniature using all three artistic techniques; the intersections between different elements represent the color mixture (laser rewriting) and erasing (laser erasing).

 figure: Fig. 6.

Fig. 6. Photos of color laser miniature paintings. (a) Interpretation of Van Gogh painting “Starry Night” and the portrait of the artist made on titanium canvas by laser paintbrush technique. (b) Laser miniature painting (author D. Lutoshina): intersections between different elements represent the color mixture (laser rewriting) and erasing (laser erasing).

Download Full Size | PPT Slide | PDF

By using the three developed basic techniques it is possible to manipulate colors and shapes of different elements. Moreover, the process of laser painting (see Visualization 1) is rather fast: average speed for colorful painting is about $7\;{\rm cm^2}$ per min (for instance, making a $3 \times 2\;{\rm cm}$ Van Gogh’s “Starry Night” took only 4 min).

Although in this article we considered only nine basic colors, there are also different possibilities to broaden the color palette and saturation range for a laser paintbrush. The first one is by managing over a wide range of laser processing parameters as was recently shown for stainless steel [40]. In Fig. S9 the alternative color palette developed for the pulse duration of $\tau = 4\; {\rm ns}$ and repetition rate $f = 99\; {\rm kHz}$ is shown. In contrast to results for 100 ns, the colors are less saturated and lie more in the blue-green-yellow region. Another possibleoption can be the addition of nanostructured and hybrid materials that are manipulated by lasers to obtain the desired optical properties [9,52]. Such colors can achieve enhanced saturation due to their resonant nature. Finally, laser fabrication of periodic surface gratings [25,26] is potentially interesting for obtaining a holographic (rainbow) effect.

4. DISCUSSION AND CONCLUSION

In contrast to previous works [30,37,39], in our experiments, for the first time to our knowledge, we obtained bright colors on titanium by heating the metal above the evaporation point. In this case, the growth of the oxide layer takes place at the cooling stage of laser processing, and the resulting thickness of the oxide strongly depends on the cooling rate. The palette of basic colors has been experimentally obtained. Colors change in a certain sequence: with the increase of cooling time, colors modify from light-yellow (${\rm Ti_1}$) to brown (${\rm Ti_6}$), and then turn to blue shades (${\rm Ti_7} - {\rm Ti_9}$). According to TEM analysis, the thickness of the oxide film has been shown to increase with the temperature increase. Simultaneously, the minima of reflection spectra redshift, which corresponds to interference effects in thin oxide film. The numerical calculation of reflection spectra demonstrated that thickness modification in the range of 13–68 nm caused spectral shift from 380 to 600 nm correspondingly. At higher temperatures the composition of the oxide layer also modifies, which supports our previous observations in [53].

A second laser pass over the already colored area leads to color rewriting or changing the original color to another one. This effect occurs in air and does not require any special atmosphere. The mechanism is based on the evaporation of the initial oxide layer during the heating stage and its repeated growth at the cooling stage. Experimentally we have shown that the new color can be obtained both by increasing of the oxide film thickness (by extending the cooling time) and by reducing of the oxide thickness. The minimum of the reflection spectrum in this case shifts either toward the UV or IR region in accordance with the thickness of the oxide film. This possibility significantly expands the potential of laser painting. Moreover, multiple color rewriting is also possible with the unlimited number of rewriting cycles. It was demonstrated that after 30 rewriting cycles neither the thickness nor composition varies, and thus observed films are identical. With the decrease of cooling time the effect of color erasing appears. The oxide film formed after the first laser pass consequently evaporates under the secondary laser pass with higher processing speed. However, the cooling rate for the scanning speed ranged from 600 to 1500 mm/s is high, and thus there is not enough time for the formation of a new oxide layer thick enough for color appearance.

Summarizing the discussed results, we have shown that within a single laser pass the oxidation process at the heating stage is followed by the evaporation of the oxide film (when the temperature exceeds the evaporation point). After that, the oxide film reforms at the cooling stage. Therefore, the cooling rate, which is linked to scanning speed, plays the main role in laser coloration, erasing, and rewriting. The longer cooling time, the thicker film that occurs. Experimental observations supported by our numerical modelling allowed us to find the interplay between rewriting and complete erasing of a color as well as to formulate the laser coloration condition [See Eq. (4)].

Therefore, by investigating the underlying physical processes, in this article we have developed an efficient artistic laser technique, recreating an equivalent to the painting paintbrush. Obtained laser paintings possess high resistance, and we believe that such scientific art will in the future become the part of our era’s heritage.

Funding

Ministry of Science and Higher Education of the Russian Federation (075-11-2019-066 of 22.11.2019).

Acknowledgment

The authors acknowledge the Interdisciplinary Resource Centre for Nanotechnology, Research Park, St. Petersburg State University for SEM measurements and lamellae preparation. Authors acknowledge the support of the Ministry of Science and Higher Education of the Russian Federation research agreement No. 075-11-2019-066 of 22.11.2019, project title "Development of high-tech production of equipment and technologies for laser coding of transported goods and their optical identification for the implementation in modern material flow management systems" (within the framework of decree of the Government of the Russian Federation No. 218 of 09.04.2010).

Disclosures

The authors declare that they have no conflicts of interest.

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

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References

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  1. W. Hong, Z. Yuan, and X. Chen, “Structural color materials for optical anticounterfeiting,” Small 16, 1907626 (2020).
    [Crossref]
  2. Y. Bao, Y. Yu, H. Xu, C. Guo, J. Li, S. Sun, Z.-K. Zhou, C.-W. Qiu, and X.-H. Wang, “Full-colour nanoprint-hologram synchronous metasurface with arbitrary hue-saturation-brightness control,” Light Sci. Appl. 8, 95 (2019).
    [Crossref]
  3. M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics,” Nat. Photonics 11, 543–554 (2017).
    [Crossref]
  4. S. V. Makarov, V. A. Milichko, I. S. Mukhin, I. I. Shishkin, D. A. Zuev, A. M. Mozharov, A. E. Krasnok, and P. A. Belov, “Controllable femtosecond laser-induced dewetting for plasmonic applications,” Laser Photon. Rev. 10, 91–99 (2016).
    [Crossref]
  5. P. Mao, C. Liu, F. Song, M. Han, S. A. Maier, and S. Zhang, “Manipulating disordered plasmonic systems by external cavity with transition from broadband absorption to reconfigurable reflection,” Nat. Commun. 11, 1538 (2020).
    [Crossref]
  6. A. Kristensen, J. K. Yang, S. I. Bozhevolnyi, S. Link, P. Nordlander, N. J. Halas, and N. A. Mortensen, “Plasmonic colour generation,” Nat. Rev. Mater. 2, 16088 (2016).
    [Crossref]
  7. Y. D. Shah, P. W. Connolly, J. P. Grant, D. Hao, C. Accarino, X. Ren, M. Kenney, V. Annese, K. G. Rew, and Z. M. Greener, “Ultralow-light-level color image reconstruction using high-efficiency plasmonic metasurface mosaic filters,” Optica 7, 632–639 (2020).
    [Crossref]
  8. C. Zou, J. Sautter, F. Setzpfandt, and I. Staude, “Resonant dielectric metasurfaces: active tuning and nonlinear effects,” J. Phys. D 52, 373002 (2019).
    [Crossref]
  9. Z. Dong, J. Ho, Y. F. Yu, Y. H. Fu, R. Paniagua-Dominguez, S. Wang, A. Kuznetsov, and J. K. Yang, “Printing beyond srgb color gamut by mimicking silicon nanostructures in free-space,” Nano Lett. 17, 7620–7628 (2017).
    [Crossref]
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    [Crossref]
  11. Y. Zhang, Q. Zhang, X. Ouyang, D. Y. Lei, A. P. Zhang, and H.-Y. Tam, “Ultrafast light-controlled growth of silver nanoparticles for direct plasmonic color printing,” ACS Nano 12, 9913–9921 (2018).
    [Crossref]
  12. K. Kumar, H. Duan, R. S. Hegde, S. C. Koh, J. N. Wei, and J. K. Yang, “Printing colour at the optical diffraction limit,” Nat. Nanotechnol. 7, 557 (2012).
    [Crossref]
  13. F. Cheng, J. Gao, T. S. Luk, and X. Yang, “Structural color printing based on plasmonic metasurfaces of perfect light absorption,” Sci. Rep. 5, 11045 (2015).
    [Crossref]
  14. D. Franklin, Y. Chen, A. Vazquez-Guardado, S. Modak, J. Boroumand, D. Xu, S.-T. Wu, and D. Chanda, “Polarization-independent actively tunable colour generation on imprinted plasmonic surfaces,” Nat. Commun. 6, 7337 (2015).
    [Crossref]
  15. J. Meng, J. J. Cadusch, and K. B. Crozier, “Detector-only spectrometer based on structurally colored silicon nanowires and a reconstruction algorithm,” Nano Lett. 20, 320–328 (2019).
    [Crossref]
  16. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
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    [Crossref]
  18. A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. Zhang, and B. Luk’Yanchuk, “Magnetic light,” Sci. Rep. 2, 492 (2012).
    [Crossref]
  19. P. Huo, M. Song, W. Zhu, C. Zhang, L. Chen, H. J. Lezec, Y. Lu, A. Agrawal, and T. Xu, “Photorealistic full-color nanopainting enabled by a low-loss metasurface,” Optica 7, 1171–1172 (2020).
    [Crossref]
  20. S. Jahani and Z. Jacob, “All-dielectric metamaterials,” Nat. Nanotechnol. 11, 23 (2016).
    [Crossref]
  21. H. Nishi and T. Tatsuma, “Full-color scattering based on plasmon and mie resonances of gold nanoparticles modulated by Fabry–Pérot interference for coloring and image projection,” ACS Appl. Nano Mater. 2, 5071–5078 (2019).
    [Crossref]
  22. Y. Jin, I. Qamar, M. Wessely, and S. Mueller, “Photo-chromeleon: re-programmable multi-color textures using photochromic dyes,” in ACM SIGGRAPH 2020 Emerging Technologies (ACM DL, 2020), pp. 1–2.
  23. Z. Liu, J. Siegel, M. Garcia-Lechuga, T. Epicier, Y. Lefkir, S. Reynaud, M. Bugnet, F. Vocanson, J. Solis, and G. Vitrant, “Three-dimensional self-organization in nanocomposite layered systems by ultrafast laser pulses,” ACS Nano 11, 5031–5040 (2017).
    [Crossref]
  24. Y. Kuroiwa and T. Tatsuma, “Laser printing of translucent plasmonic full-color images with transmission-scattering dichroism of silver nanoparticles,” ACS Appl. Nano Mater. 3, 2472–2479 (2020).
    [Crossref]
  25. A. Y. Vorobyev and C. Guo, “Colorizing metals with femtosecond laser pulses,” Appl. Phys. Lett. 92, 041914 (2008).
    [Crossref]
  26. E. Ageev, V. Veiko, E. Vlasova, Y. Karlagina, A. Krivonosov, M. Moskvin, G. Odintsova, V. Pshenichnov, V. Romanov, and R. Yatsuk, “Controlled nanostructures formation on stainless steel by short laser pulses for products protection against falsification,” Opt. Express 26, 2117–2122 (2018).
    [Crossref]
  27. B. Dusser, Z. Sagan, H. Soder, N. Faure, J.-P. Colombier, M. Jourlin, and E. Audouard, “Controlled nanostructrures formation by ultra fast laser pulses for color marking,” Opt. Express 18, 2913–2924 (2010).
    [Crossref]
  28. H. Jiang and B. Kaminska, “Scalable inkjet-based structural color printing by molding transparent gratings on multilayer nanostructured surfaces,” ACS Nano 12, 3112–3125 (2018).
    [Crossref]
  29. K. Keller, A. V. Yakovlev, E. V. Grachova, and A. V. Vinogradov, “Inkjet printing of multicolor daylight visible opal holography,” Adv. Funct. Mater. 28, 1706903 (2018).
    [Crossref]
  30. V. Veiko, G. Odintsova, E. Gorbunova, E. Ageev, A. Shimko, Y. Karlagina, and Y. Andreeva, “Development of complete color palette based on spectrophotometric measurements of steel oxidation results for enhancement of color laser marking technology,” Mater. Des. 89, 684–688 (2016).
    [Crossref]
  31. A. V. Yakovlev, V. A. Milichko, V. V. Vinogradov, and A. V. Vinogradov, “Inkjet color printing by interference nanostructures,” ACS Nano 10, 3078–3086 (2016).
    [Crossref]
  32. K. Łęcka, M. Wójcik, and A. Antończak, “Laser-induced color marking of titanium: a modeling study of the interference effect and the impact of protective coating,” Math. Probl. Eng. 2017, 3425108 (2017).
    [Crossref]
  33. H. Liu, W. Lin, and M. Hong, “Surface coloring by laser irradiation of solid substrates,” APL Photon. 4, 051101 (2019).
    [Crossref]
  34. R. Zhou, T. Huang, Y. Lu, and M. Hong, “Tunable coloring via post-thermal annealing of laser-processed metal surface,” Appl. Sci. 8, 1716 (2018).
    [Crossref]
  35. K. ŁeRcka, A. Antonczak, B. Szubzda, M. Wójcik, B. SteRpak, P. Szymczyk, M. Trzcinski, M. Ozimek, and K. Abramski, “Effects of laser-induced oxidation on the corrosion resistance of aisi 304 stainless steel,” J. Laser Appl. 28, 032009 (2016).
    [Crossref]
  36. V. Veiko, G. Odintsova, E. Ageev, Y. Karlagina, A. Loginov, A. Skuratova, and E. Gorbunova, “Controlled oxide films formation by nanosecond laser pulses for color marking,” Opt. Express 22, 24342–24347 (2014).
    [Crossref]
  37. E. Amara, F. Haïd, and A. Noukaz, “Experimental investigations on fiber laser color marking of steels,” Appl. Surf. Sci. 351, 1–12 (2015).
    [Crossref]
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2020 (7)

W. Hong, Z. Yuan, and X. Chen, “Structural color materials for optical anticounterfeiting,” Small 16, 1907626 (2020).
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Y. D. Shah, P. W. Connolly, J. P. Grant, D. Hao, C. Accarino, X. Ren, M. Kenney, V. Annese, K. G. Rew, and Z. M. Greener, “Ultralow-light-level color image reconstruction using high-efficiency plasmonic metasurface mosaic filters,” Optica 7, 632–639 (2020).
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P. Mao, C. Liu, F. Song, M. Han, S. A. Maier, and S. Zhang, “Manipulating disordered plasmonic systems by external cavity with transition from broadband absorption to reconfigurable reflection,” Nat. Commun. 11, 1538 (2020).
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P. Huo, M. Song, W. Zhu, C. Zhang, L. Chen, H. J. Lezec, Y. Lu, A. Agrawal, and T. Xu, “Photorealistic full-color nanopainting enabled by a low-loss metasurface,” Optica 7, 1171–1172 (2020).
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Y. Kuroiwa and T. Tatsuma, “Laser printing of translucent plasmonic full-color images with transmission-scattering dichroism of silver nanoparticles,” ACS Appl. Nano Mater. 3, 2472–2479 (2020).
[Crossref]

S. Cucerca, P. Didyk, H.-P. Seidel, and V. Babaei, “Computational image marking on metals via laser induced heating,” ACM Trans. Graph. 39, 70–71 (2020).
[Crossref]

J. Trisno, R. Ng, Q. Ruan, C. Qiu, N. Mortensen, and J. Yang, “Nanophotonic structural colors,” ACS Photon. 8, 18–33 (2020).
[Crossref]

2019 (6)

G. Odintsova, Y. Andreeva, A. Salminen, H. Roozbahani, L. Van Cuong, R. Yatsuk, V. Golubeva, V. Romanov, and V. Veiko, “Investigation of production related impact on the optical properties of color laser marking,” J. Mater. Process. Technol. 274, 116263 (2019).
[Crossref]

H. Nishi and T. Tatsuma, “Full-color scattering based on plasmon and mie resonances of gold nanoparticles modulated by Fabry–Pérot interference for coloring and image projection,” ACS Appl. Nano Mater. 2, 5071–5078 (2019).
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H. Liu, W. Lin, and M. Hong, “Surface coloring by laser irradiation of solid substrates,” APL Photon. 4, 051101 (2019).
[Crossref]

J. Meng, J. J. Cadusch, and K. B. Crozier, “Detector-only spectrometer based on structurally colored silicon nanowires and a reconstruction algorithm,” Nano Lett. 20, 320–328 (2019).
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C. Zou, J. Sautter, F. Setzpfandt, and I. Staude, “Resonant dielectric metasurfaces: active tuning and nonlinear effects,” J. Phys. D 52, 373002 (2019).
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Y. Bao, Y. Yu, H. Xu, C. Guo, J. Li, S. Sun, Z.-K. Zhou, C.-W. Qiu, and X.-H. Wang, “Full-colour nanoprint-hologram synchronous metasurface with arbitrary hue-saturation-brightness control,” Light Sci. Appl. 8, 95 (2019).
[Crossref]

2018 (6)

Y. Zhang, Q. Zhang, X. Ouyang, D. Y. Lei, A. P. Zhang, and H.-Y. Tam, “Ultrafast light-controlled growth of silver nanoparticles for direct plasmonic color printing,” ACS Nano 12, 9913–9921 (2018).
[Crossref]

R. Zhou, T. Huang, Y. Lu, and M. Hong, “Tunable coloring via post-thermal annealing of laser-processed metal surface,” Appl. Sci. 8, 1716 (2018).
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H. Jiang and B. Kaminska, “Scalable inkjet-based structural color printing by molding transparent gratings on multilayer nanostructured surfaces,” ACS Nano 12, 3112–3125 (2018).
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K. Keller, A. V. Yakovlev, E. V. Grachova, and A. V. Vinogradov, “Inkjet printing of multicolor daylight visible opal holography,” Adv. Funct. Mater. 28, 1706903 (2018).
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E. Ageev, V. Veiko, E. Vlasova, Y. Karlagina, A. Krivonosov, M. Moskvin, G. Odintsova, V. Pshenichnov, V. Romanov, and R. Yatsuk, “Controlled nanostructures formation on stainless steel by short laser pulses for products protection against falsification,” Opt. Express 26, 2117–2122 (2018).
[Crossref]

T. Jwad, M. Walker, and S. Dimov, “Erasing and rewriting of titanium oxide colour marks using laser-induced reduction/oxidation,” Appl. Surf. Sci. 458, 849–854 (2018).
[Crossref]

2017 (6)

K. Łęcka, M. Wójcik, and A. Antończak, “Laser-induced color marking of titanium: a modeling study of the interference effect and the impact of protective coating,” Math. Probl. Eng. 2017, 3425108 (2017).
[Crossref]

E. Ageev, Y. M. Andreeva, Y. Y. Karlagina, Y. R. Kolobov, S. Manokhin, G. Odintsova, A. Slobodov, and V. Veiko, “Composition analysis of oxide films formed on titanium surface under pulsed laser action by method of chemical thermodynamics,” Laser Phys. 27, 046001 (2017).
[Crossref]

S. A. Jalil, M. Akram, G. Yoon, A. Khalid, D. Lee, N. Raeis-Hosseini, S. So, I. Kim, Q. S. Ahmed, and J. Rho, “High refractive index Ti3O5 films for dielectric metasurfaces,” Chin. Phys. Lett. 34, 088102 (2017).
[Crossref]

Z. Liu, J. Siegel, M. Garcia-Lechuga, T. Epicier, Y. Lefkir, S. Reynaud, M. Bugnet, F. Vocanson, J. Solis, and G. Vitrant, “Three-dimensional self-organization in nanocomposite layered systems by ultrafast laser pulses,” ACS Nano 11, 5031–5040 (2017).
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M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics,” Nat. Photonics 11, 543–554 (2017).
[Crossref]

Z. Dong, J. Ho, Y. F. Yu, Y. H. Fu, R. Paniagua-Dominguez, S. Wang, A. Kuznetsov, and J. K. Yang, “Printing beyond srgb color gamut by mimicking silicon nanostructures in free-space,” Nano Lett. 17, 7620–7628 (2017).
[Crossref]

2016 (8)

S. V. Makarov, V. A. Milichko, I. S. Mukhin, I. I. Shishkin, D. A. Zuev, A. M. Mozharov, A. E. Krasnok, and P. A. Belov, “Controllable femtosecond laser-induced dewetting for plasmonic applications,” Laser Photon. Rev. 10, 91–99 (2016).
[Crossref]

A. Kristensen, J. K. Yang, S. I. Bozhevolnyi, S. Link, P. Nordlander, N. J. Halas, and N. A. Mortensen, “Plasmonic colour generation,” Nat. Rev. Mater. 2, 16088 (2016).
[Crossref]

X. Zhu, C. Vannahme, E. Højlund-Nielsen, N. A. Mortensen, and A. Kristensen, “Plasmonic colour laser printing,” Nat. Nanotechnol. 11, 325 (2016).
[Crossref]

S. Jahani and Z. Jacob, “All-dielectric metamaterials,” Nat. Nanotechnol. 11, 23 (2016).
[Crossref]

V. Veiko, G. Odintsova, E. Gorbunova, E. Ageev, A. Shimko, Y. Karlagina, and Y. Andreeva, “Development of complete color palette based on spectrophotometric measurements of steel oxidation results for enhancement of color laser marking technology,” Mater. Des. 89, 684–688 (2016).
[Crossref]

A. V. Yakovlev, V. A. Milichko, V. V. Vinogradov, and A. V. Vinogradov, “Inkjet color printing by interference nanostructures,” ACS Nano 10, 3078–3086 (2016).
[Crossref]

K. ŁeRcka, A. Antonczak, B. Szubzda, M. Wójcik, B. SteRpak, P. Szymczyk, M. Trzcinski, M. Ozimek, and K. Abramski, “Effects of laser-induced oxidation on the corrosion resistance of aisi 304 stainless steel,” J. Laser Appl. 28, 032009 (2016).
[Crossref]

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780–1786 (2016).
[Crossref]

2015 (4)

J. Jaglarz, J. Szewczenko, K. Marszałek, M. Basiaga, M. Marszałek, and R. Gaweł, “Nonstandard optical methods as a tool for rough surface analysis,” Mater. Today 2(7), 4046–4052 (2015).
[Crossref]

E. Amara, F. Haïd, and A. Noukaz, “Experimental investigations on fiber laser color marking of steels,” Appl. Surf. Sci. 351, 1–12 (2015).
[Crossref]

F. Cheng, J. Gao, T. S. Luk, and X. Yang, “Structural color printing based on plasmonic metasurfaces of perfect light absorption,” Sci. Rep. 5, 11045 (2015).
[Crossref]

D. Franklin, Y. Chen, A. Vazquez-Guardado, S. Modak, J. Boroumand, D. Xu, S.-T. Wu, and D. Chanda, “Polarization-independent actively tunable colour generation on imprinted plasmonic surfaces,” Nat. Commun. 6, 7337 (2015).
[Crossref]

2014 (1)

2013 (2)

M. Rahmani, B. Luk’yanchuk, and M. Hong, “Fano resonance in novel plasmonic nanostructures,” Laser Photon. Rev. 7, 329–349 (2013).
[Crossref]

M. R. Saleem, R. Ali, S. Honkanen, and J. Turunen, “Thermal properties of thin al2o3 films and their barrier layer effect on thermo-optic properties of TiO2 films grown by atomic layer deposition,” Thin Solid Films 542, 257–262 (2013).
[Crossref]

2012 (2)

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. Zhang, and B. Luk’Yanchuk, “Magnetic light,” Sci. Rep. 2, 492 (2012).
[Crossref]

K. Kumar, H. Duan, R. S. Hegde, S. C. Koh, J. N. Wei, and J. K. Yang, “Printing colour at the optical diffraction limit,” Nat. Nanotechnol. 7, 557 (2012).
[Crossref]

2010 (1)

2009 (1)

D. Höche, S. Müller, G. Rapin, M. Shinn, E. Remdt, M. Gubisch, and P. Schaaf, “Marangoni convection during free electron laser nitriding of titanium,” Metall. Mater. Trans. B 40, 497–507 (2009).
[Crossref]

2008 (1)

A. Y. Vorobyev and C. Guo, “Colorizing metals with femtosecond laser pulses,” Appl. Phys. Lett. 92, 041914 (2008).
[Crossref]

2004 (1)

A. Pereira, A. Cros, P. Delaporte, S. Georgiou, A. Manousaki, W. Marine, and M. Sentis, “Surface nanostructuring of metals by laser irradiation: effects of pulse duration, wavelength and gas atmosphere,” Appl. Phys. A 79, 1433–1437 (2004).
[Crossref]

2001 (1)

N. Bulgakova and A. Bulgakov, “Pulsed laser ablation of solids: transition from normal vaporization to phase explosion,” Appl. Phys. A 73, 199–208 (2001).
[Crossref]

1999 (1)

A. Bendavid, P. Martin, A. Jamting, and H. Takikawa, “Structural and optical properties of titanium oxide thin films deposited by filtered arc deposition,” Thin Solid Films 355, 6–11 (1999).
[Crossref]

1961 (1)

P. Kofstad, P. Anderson, and O. Krudtaa, “Oxidation of titanium in the temperature range 800–1200 c,” J. Less Common Met. 3, 89–97 (1961).
[Crossref]

Abramski, K.

K. ŁeRcka, A. Antonczak, B. Szubzda, M. Wójcik, B. SteRpak, P. Szymczyk, M. Trzcinski, M. Ozimek, and K. Abramski, “Effects of laser-induced oxidation on the corrosion resistance of aisi 304 stainless steel,” J. Laser Appl. 28, 032009 (2016).
[Crossref]

Accarino, C.

Ageev, E.

E. Ageev, V. Veiko, E. Vlasova, Y. Karlagina, A. Krivonosov, M. Moskvin, G. Odintsova, V. Pshenichnov, V. Romanov, and R. Yatsuk, “Controlled nanostructures formation on stainless steel by short laser pulses for products protection against falsification,” Opt. Express 26, 2117–2122 (2018).
[Crossref]

E. Ageev, Y. M. Andreeva, Y. Y. Karlagina, Y. R. Kolobov, S. Manokhin, G. Odintsova, A. Slobodov, and V. Veiko, “Composition analysis of oxide films formed on titanium surface under pulsed laser action by method of chemical thermodynamics,” Laser Phys. 27, 046001 (2017).
[Crossref]

V. Veiko, G. Odintsova, E. Gorbunova, E. Ageev, A. Shimko, Y. Karlagina, and Y. Andreeva, “Development of complete color palette based on spectrophotometric measurements of steel oxidation results for enhancement of color laser marking technology,” Mater. Des. 89, 684–688 (2016).
[Crossref]

V. Veiko, G. Odintsova, E. Ageev, Y. Karlagina, A. Loginov, A. Skuratova, and E. Gorbunova, “Controlled oxide films formation by nanosecond laser pulses for color marking,” Opt. Express 22, 24342–24347 (2014).
[Crossref]

Agrawal, A.

Ahmed, Q. S.

S. A. Jalil, M. Akram, G. Yoon, A. Khalid, D. Lee, N. Raeis-Hosseini, S. So, I. Kim, Q. S. Ahmed, and J. Rho, “High refractive index Ti3O5 films for dielectric metasurfaces,” Chin. Phys. Lett. 34, 088102 (2017).
[Crossref]

Akram, M.

S. A. Jalil, M. Akram, G. Yoon, A. Khalid, D. Lee, N. Raeis-Hosseini, S. So, I. Kim, Q. S. Ahmed, and J. Rho, “High refractive index Ti3O5 films for dielectric metasurfaces,” Chin. Phys. Lett. 34, 088102 (2017).
[Crossref]

Ali, R.

M. R. Saleem, R. Ali, S. Honkanen, and J. Turunen, “Thermal properties of thin al2o3 films and their barrier layer effect on thermo-optic properties of TiO2 films grown by atomic layer deposition,” Thin Solid Films 542, 257–262 (2013).
[Crossref]

Amara, E.

E. Amara, F. Haïd, and A. Noukaz, “Experimental investigations on fiber laser color marking of steels,” Appl. Surf. Sci. 351, 1–12 (2015).
[Crossref]

Anderson, P.

P. Kofstad, P. Anderson, and O. Krudtaa, “Oxidation of titanium in the temperature range 800–1200 c,” J. Less Common Met. 3, 89–97 (1961).
[Crossref]

Andreeva, Y.

G. Odintsova, Y. Andreeva, A. Salminen, H. Roozbahani, L. Van Cuong, R. Yatsuk, V. Golubeva, V. Romanov, and V. Veiko, “Investigation of production related impact on the optical properties of color laser marking,” J. Mater. Process. Technol. 274, 116263 (2019).
[Crossref]

V. Veiko, G. Odintsova, E. Gorbunova, E. Ageev, A. Shimko, Y. Karlagina, and Y. Andreeva, “Development of complete color palette based on spectrophotometric measurements of steel oxidation results for enhancement of color laser marking technology,” Mater. Des. 89, 684–688 (2016).
[Crossref]

Andreeva, Y. M.

E. Ageev, Y. M. Andreeva, Y. Y. Karlagina, Y. R. Kolobov, S. Manokhin, G. Odintsova, A. Slobodov, and V. Veiko, “Composition analysis of oxide films formed on titanium surface under pulsed laser action by method of chemical thermodynamics,” Laser Phys. 27, 046001 (2017).
[Crossref]

Annese, V.

Antonczak, A.

K. Łęcka, M. Wójcik, and A. Antończak, “Laser-induced color marking of titanium: a modeling study of the interference effect and the impact of protective coating,” Math. Probl. Eng. 2017, 3425108 (2017).
[Crossref]

K. ŁeRcka, A. Antonczak, B. Szubzda, M. Wójcik, B. SteRpak, P. Szymczyk, M. Trzcinski, M. Ozimek, and K. Abramski, “Effects of laser-induced oxidation on the corrosion resistance of aisi 304 stainless steel,” J. Laser Appl. 28, 032009 (2016).
[Crossref]

Audouard, E.

Babaei, V.

S. Cucerca, P. Didyk, H.-P. Seidel, and V. Babaei, “Computational image marking on metals via laser induced heating,” ACM Trans. Graph. 39, 70–71 (2020).
[Crossref]

Bao, Y.

Y. Bao, Y. Yu, H. Xu, C. Guo, J. Li, S. Sun, Z.-K. Zhou, C.-W. Qiu, and X.-H. Wang, “Full-colour nanoprint-hologram synchronous metasurface with arbitrary hue-saturation-brightness control,” Light Sci. Appl. 8, 95 (2019).
[Crossref]

Basiaga, M.

J. Jaglarz, J. Szewczenko, K. Marszałek, M. Basiaga, M. Marszałek, and R. Gaweł, “Nonstandard optical methods as a tool for rough surface analysis,” Mater. Today 2(7), 4046–4052 (2015).
[Crossref]

Belov, P. A.

S. V. Makarov, V. A. Milichko, I. S. Mukhin, I. I. Shishkin, D. A. Zuev, A. M. Mozharov, A. E. Krasnok, and P. A. Belov, “Controllable femtosecond laser-induced dewetting for plasmonic applications,” Laser Photon. Rev. 10, 91–99 (2016).
[Crossref]

Bendavid, A.

A. Bendavid, P. Martin, A. Jamting, and H. Takikawa, “Structural and optical properties of titanium oxide thin films deposited by filtered arc deposition,” Thin Solid Films 355, 6–11 (1999).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999), Chap. 1.

Boroumand, J.

D. Franklin, Y. Chen, A. Vazquez-Guardado, S. Modak, J. Boroumand, D. Xu, S.-T. Wu, and D. Chanda, “Polarization-independent actively tunable colour generation on imprinted plasmonic surfaces,” Nat. Commun. 6, 7337 (2015).
[Crossref]

Bozhevolnyi, S. I.

A. Kristensen, J. K. Yang, S. I. Bozhevolnyi, S. Link, P. Nordlander, N. J. Halas, and N. A. Mortensen, “Plasmonic colour generation,” Nat. Rev. Mater. 2, 16088 (2016).
[Crossref]

Bugnet, M.

Z. Liu, J. Siegel, M. Garcia-Lechuga, T. Epicier, Y. Lefkir, S. Reynaud, M. Bugnet, F. Vocanson, J. Solis, and G. Vitrant, “Three-dimensional self-organization in nanocomposite layered systems by ultrafast laser pulses,” ACS Nano 11, 5031–5040 (2017).
[Crossref]

Bulgakov, A.

N. Bulgakova and A. Bulgakov, “Pulsed laser ablation of solids: transition from normal vaporization to phase explosion,” Appl. Phys. A 73, 199–208 (2001).
[Crossref]

Bulgakova, N.

N. Bulgakova and A. Bulgakov, “Pulsed laser ablation of solids: transition from normal vaporization to phase explosion,” Appl. Phys. A 73, 199–208 (2001).
[Crossref]

Cadusch, J. J.

J. Meng, J. J. Cadusch, and K. B. Crozier, “Detector-only spectrometer based on structurally colored silicon nanowires and a reconstruction algorithm,” Nano Lett. 20, 320–328 (2019).
[Crossref]

Chanda, D.

D. Franklin, Y. Chen, A. Vazquez-Guardado, S. Modak, J. Boroumand, D. Xu, S.-T. Wu, and D. Chanda, “Polarization-independent actively tunable colour generation on imprinted plasmonic surfaces,” Nat. Commun. 6, 7337 (2015).
[Crossref]

Chen, L.

Chen, X.

W. Hong, Z. Yuan, and X. Chen, “Structural color materials for optical anticounterfeiting,” Small 16, 1907626 (2020).
[Crossref]

Chen, Y.

D. Franklin, Y. Chen, A. Vazquez-Guardado, S. Modak, J. Boroumand, D. Xu, S.-T. Wu, and D. Chanda, “Polarization-independent actively tunable colour generation on imprinted plasmonic surfaces,” Nat. Commun. 6, 7337 (2015).
[Crossref]

Cheng, F.

F. Cheng, J. Gao, T. S. Luk, and X. Yang, “Structural color printing based on plasmonic metasurfaces of perfect light absorption,” Sci. Rep. 5, 11045 (2015).
[Crossref]

Colombier, J.-P.

Connolly, P. W.

Cros, A.

A. Pereira, A. Cros, P. Delaporte, S. Georgiou, A. Manousaki, W. Marine, and M. Sentis, “Surface nanostructuring of metals by laser irradiation: effects of pulse duration, wavelength and gas atmosphere,” Appl. Phys. A 79, 1433–1437 (2004).
[Crossref]

Crozier, K. B.

J. Meng, J. J. Cadusch, and K. B. Crozier, “Detector-only spectrometer based on structurally colored silicon nanowires and a reconstruction algorithm,” Nano Lett. 20, 320–328 (2019).
[Crossref]

Cucerca, S.

S. Cucerca, P. Didyk, H.-P. Seidel, and V. Babaei, “Computational image marking on metals via laser induced heating,” ACM Trans. Graph. 39, 70–71 (2020).
[Crossref]

Delaporte, P.

A. Pereira, A. Cros, P. Delaporte, S. Georgiou, A. Manousaki, W. Marine, and M. Sentis, “Surface nanostructuring of metals by laser irradiation: effects of pulse duration, wavelength and gas atmosphere,” Appl. Phys. A 79, 1433–1437 (2004).
[Crossref]

Didyk, P.

S. Cucerca, P. Didyk, H.-P. Seidel, and V. Babaei, “Computational image marking on metals via laser induced heating,” ACM Trans. Graph. 39, 70–71 (2020).
[Crossref]

Dietrich, K.

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780–1786 (2016).
[Crossref]

Dimov, S.

T. Jwad, M. Walker, and S. Dimov, “Erasing and rewriting of titanium oxide colour marks using laser-induced reduction/oxidation,” Appl. Surf. Sci. 458, 849–854 (2018).
[Crossref]

Dong, Z.

Z. Dong, J. Ho, Y. F. Yu, Y. H. Fu, R. Paniagua-Dominguez, S. Wang, A. Kuznetsov, and J. K. Yang, “Printing beyond srgb color gamut by mimicking silicon nanostructures in free-space,” Nano Lett. 17, 7620–7628 (2017).
[Crossref]

Duan, H.

K. Kumar, H. Duan, R. S. Hegde, S. C. Koh, J. N. Wei, and J. K. Yang, “Printing colour at the optical diffraction limit,” Nat. Nanotechnol. 7, 557 (2012).
[Crossref]

Dusser, B.

Epicier, T.

Z. Liu, J. Siegel, M. Garcia-Lechuga, T. Epicier, Y. Lefkir, S. Reynaud, M. Bugnet, F. Vocanson, J. Solis, and G. Vitrant, “Three-dimensional self-organization in nanocomposite layered systems by ultrafast laser pulses,” ACS Nano 11, 5031–5040 (2017).
[Crossref]

Faure, N.

Franklin, D.

D. Franklin, Y. Chen, A. Vazquez-Guardado, S. Modak, J. Boroumand, D. Xu, S.-T. Wu, and D. Chanda, “Polarization-independent actively tunable colour generation on imprinted plasmonic surfaces,” Nat. Commun. 6, 7337 (2015).
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Supplementary Material (2)

NameDescription
» Supplement 1       Supplementary information for the manuscript
» Visualization 1       The video shows the process of laser painting on titanium. By nanosecond pulsed irradiation it is possible to draw a colorful picture, change colors, and erase them completely. These processes are possible due to the material heating above [Read More]

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (6)

Fig. 1.
Fig. 1. Schematics of laser paintbrush and microimages of color strokes.
Fig. 2.
Fig. 2. Principle of color laser paintbrush. (a) Applying of color strokes: schematics of the process and photo of the color palette for titanium: laser intensity $I = 1.02 \cdot {10^7} \; {\rm W}/{\rm cm^2}$, and scanning speed decreases from 500 to $100\;{\rm mm/s}$ with the step of $50\;{\rm mm/s}$ for colors ${\rm Ti_1}$ to ${\rm Ti_9}$, respectively. (b) Reflectance spectra of the obtained color palette. (c) Color palette on color locus. (d) Schematics of laser rewriting and photo of color rewriting: eight identical areas of ${{\rm Ti}_8}$ color were initially obtained. After that, the second laser pass ($I = 1.02 \cdot {10^7} \; {\rm W}/{\rm cm^2}$) with the scanning speed in the range of 100–1500 mm/s was performed; the intersection area surrounded by black dashed line represents the corrected color. (e) Schematics of laser color erasing, photo, and microimages of color erasing of different colors ${\rm Ti_2} - {\rm Ti_9}$ performed at scanning speed ${V_{\textit{sc}}} = 1500\; {\rm mm/s}$ ($I = 1.02 \cdot {10^7}\; {\rm W}/{\rm cm^2}$).
Fig. 3.
Fig. 3. Color maps for laser painting, color change, and erasing for $I = 1.02 \cdot {10^7} \; {\rm W}/{\rm cm^2}$. (a) Color palette of the laser paintbrush. The map represents color dependencies on different scanning speed: the single-step coloration regime on a bare titanium (coloring zone), the change of eight initial colors for other ones (color change zone), complete erasing of colors (erasing zone). (b) Multiple rewriting of the color circle: colors are changed in a consequence, the result after initial writing (first pass), and rewriting (second and third passes).
Fig. 4.
Fig. 4. Multiple color rewriting. (a) Schematics of laser multiple rewriting of gold color to blue and back. (b) Photo of rewritten squares: Layer 1 (${\rm L}1$) reproduces sample ${\rm Ti_4}$ (${I} = 1.02 \cdot {10^7}\; {\rm W}/{\rm cm^2}$, ${V_{\textit{sc}}} = 350\; {\rm mm/s}$). All the blue layers (${\rm L2,L4,L6,L8}$) were produced by reprocessing of gold areas with a scanning speed of ${V_{\textit{sc}}} = 170\; {\rm mm/s}$. The ${\rm L3,L5,L7,L9}$ gold layers were recorded with a scanning speed of ${V_{{sc}}} = 450\;{\rm mm/s}$. (c)–(e) Reflectance spectra of colors: (c) experimental spectra, ${\rm L1 - L9}$: color difference between the rewritten colors $\Delta E$ does not exceed 8; (d) colors representing experimental and calculated CIE ${\rm L*a*b*}$ (2013) color coordinates for initial surface (${\rm Ti_0}$) L1 and L8; (e) modelled spectra: the yellow line is for the ${\rm L}1$ regime (estimated for $20 \pm 3\;{\rm nm}$ thick rutile film on a bulk Ti), the and blue line is for the ${\rm L}8$ regime (estimated for $23 \pm 3\;{\rm nm}$ thick ${\rm Ti_3}{\rm O_5}$ and $12 \pm 2\;{\rm nm}$ thick anatase films layered on top of a bulk Ti). (f)–(h) Morphological and structural characterization of oxide layers after laser exposure. TEM, STEM, and electron beam diffraction images of oxide films of samples: (f) ${\rm L}1$, (g) L9, and (h)${\rm Ti_8}$.
Fig. 5.
Fig. 5. Temperature distribution and laser oxidation process. (a) Microimage and profile of Ti surface after laser irradiation; (b) calculated temperature distribution over the surface; (c) temperature dynamics for central region of the recorded track considering the presence of oxide layers for different scanning speeds (${I} = 1.02 \cdot {10^7} \;{\rm W}/{\rm cm^2}$).
Fig. 6.
Fig. 6. Photos of color laser miniature paintings. (a) Interpretation of Van Gogh painting “Starry Night” and the portrait of the artist made on titanium canvas by laser paintbrush technique. (b) Laser miniature painting (author D. Lutoshina): intersections between different elements represent the color mixture (laser rewriting) and erasing (laser erasing).

Equations (4)

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M = [ cos ( β 1 ) cos ( β 2 ) n 2 n 1 sin ( β 1 ) sin ( β 2 ) i ( sin ( β 2 ) cos ( β 1 ) n 2 + cos ( β 2 ) sin ( β 1 ) n 1 ) i ( n 2 sin ( β 2 ) + cos ( β 1 ) n 1 cos ( β 2 ) sin ( β 1 ) ) cos ( β 1 ) cos ( β 2 ) n 2 n 1 sin ( β 1 ) sin ( β 2 ) ] ,
R ( λ , h j ) = | M 1 , 1 + n 3 M 1 , 2 M 2 , 1 n 3 M 2 , 2 M 1 , 1 + n 3 M 1 , 2 + M 2 , 1 + n 3 M 2 , 2 | 2 ,
( c + L m δ ( T T m ) ) T t ( k T ) = 0 k T z | z = 0 = A i = 0 N 1 q i ν e ν L e ν k T x | x = 0 = 0 k T y | y = 0 = 0 k T z | z = z max = 0 k T x | x = x max = 0 k T y | y = y max = 0 T | t = 0 = T 0 ,
2 10 5 I + 393 V sc > 1 ,